where \(L^{(1)}[Q]\)  can be identified as the conservative Lagrangian.
This result is in agreement with Eq.206 and Eq.208 of [1]}. Analogously, we can rewrite the result for the double-emission diagram from Eq.(REF ), as:
\(S_{eff\ 5PN}^{Q_+Q_+Q_-2 } \ &=& \ \int \ dt \ \biggl (L^{(2)}[Q_1]-L^{(2)}[Q_2]+R^{(2)}[Q_1,Q_2] \biggr ) \ , \\L^{(2)}[Q_1]& = & \frac{G_N^2}{8} Tr\biggl [Q_1Q_1^{(4)}Q_1^{(4)}\biggr ] \ , \\R^{(2)}[Q_1,Q_2] & = & G_N^2 Tr\biggl [-\frac{1}{4}Q_1Q_1^{(4)}Q_2^{(4)}+\frac{3}{8}Q_2Q_1^{(4)}Q_1^{(4)}\biggr ] -(1\leftrightarrow 2 ) \ ,\) 
